The critical behavior of an ionic liquid-in-oil (IL-O) microemulsion of 1-butyl-3-methylimidazolium tetrafluoroborate [bmim] [BF4] (IL), cyclohexane, and the nonionic surfactant polyoxyethylene tert-octylphenyl ether (T-X100) was studied for the first time. The coexistence curves of (T, n) and (T, Phi) (n and Phi are refractive index and volume fraction of the fraction of the volume of IL and T-X100 to the total volume of the system, respectively) for an IL-O microemulsion at constant pressure and a constant molar ratio (omega) of IL to T-X100 have been determined by measurements of the refractive index. The critical exponent beta was deduced precisely from (T, n) and (T, 43) coexistence curves. These values were 0.329 and 0.330, respectively, and were consistent with the 3D Ising exponent within experimental uncertainties. The refractive index (n) is a better choice of the concentration variable than the volume fraction (Phi) used for the construction of the order parameter to fit the Ising behavior.